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This paper uses 3D grain-scale finite element (FE) simulations to appraise the classical scattering theory of plane longitudinal wave propagation in untextured polycrystals with statistically equiaxed grains belonging to the seven crystal symmetries. As revealed from the results of 10,390 materials, the classical theory has a linear relationship with the elastic scattering factor at the quasi-static velocity limit, whereas the reference FE and self-consistent (SC) results generally exhibit a quadratic relationship. As supported by the results of 90 materials, such order difference also extends to the attenuation and phase velocity, leading to larger differences between the classical theory and the FE results for more strongly scattering materials. Alternatively, two approximate models are proposed to achieve more accurate calculations by including an additional quadratic term. One model uses quadratic coefficients from quasi-static SC velocity fits and is thus symmetry-specific, while the other uses theoretically-determined coefficients and is valid for any individual material. These simple models generally deliver more accurate attenuation and phase velocity (particularly the second model) than the classical theory, especially for strongly scattering materials. However, the models are invalid for the attenuation of materials with negative quadratic coefficients., Comment: 26 pages, 6 figures, 5 tables, submitted to Philosophical Transactions of the Royal Society A

This work studies scattering-induced elastic wave attenuation and phase velocity variation in 3D untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation models and the grain-scale finite element (FE) model, pushing the boundary towards strongly scattering materials. The results for materials with Zener anisotropy indices A>1 show a good agreement between the theoretical and FE models in the transition and stochastic regions. In the Rayleigh regime, the agreement is reasonable for common structural materials with 11, a semi-analytical model is proposed by iterating the far-field Born approximation and optimising the iterative coefficient. The proposed model agrees remarkably well with the FE model across all studied materials with greatly differing microstructures; the model validity also extends to the quasi-static velocity limit. For polycrystals with A<1, it is found that the agreement between the SOA and FE results is excellent for all studied materials and the correction of the model is not needed., Comment: 26 pages, 9 figures, 3 tables, submitted to Proceedings of the Royal Society A

In this report analytical and numerical methods are proposed to estimate the effective elastic properties of regular and random open-cell foams. The methods are based on the principle of minimum energy and on structural beam models. The analytical solutions are obtained using symbolic processing software. The microstructure of the random foam is simulated using Voronoi tessellation together with a rate-dependent random close-packing algorithm. The statistics of the geometrical properties of random foams corresponding to different packing fractions have been studied. The effects of the packing fraction on elastic properties of the foams have been investigated by decomposing the compliance into bending and axial compliance components. It is shown that the bending compliance increases and the axial compliance decreases when the packing fraction increases. Keywords: Foam; Elastic properties; Finite element; Randomness

Experimental study conducted on thermo-oxidative degradation of composite-material specimens made of silicon carbide fibers in matrices of reaction-bonded silicon nitride. In SiC/Si3N4 composites of study, interphase is 3-micrometers-thick carbon-rich coat on surface of each SiC fiber. Thermo-oxidative degradation of these composites involves diffusion of oxygen through pores of composites to interphases damaged by oxidation. Nondestructive tests reveal critical exposure times.